The graph G1 is a planar connected graph. It has 24 edges, and 8 faces. How many vertices does G1 have? ______ Suppose the graph is planar but not connected and has 4 components. Derive a variant of Euler’s formula for this case. v - e + f = _____

Q: 5. Evaluate the integral F.dS where F = (2x, y, z) and S is the boundary of the solid cylinder x² +…

A: Given  F→= 2x,y,z       equation of boundary of the cylinder is x2+y2=1…

Q: -4t² + 16t + 9 f(t) = -4t²

A:

Q: The biggest cause of inventory loss, called shrinkage, is shoplifting, followed closely by employee…

A: We have to find the required sets.

Q: Let A and B be matrices of relevant dimensions, and AB = 0. Can we say that the columns of B are in…

A:

Q: Suppose a triangle has the following vertices: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0)…

A: As per the question we are given the following 3d coordinates of a triangle as : v1 = (-2, 3, 6) v2…

Q: Exercise 5.5.8 Explain why an nxn matrix A is both one to one and onto if and only if its rank is n.

A:

Q: Until recently, all area codes had a 0 or a 1 as the middle digit and the first digit could not be 0…

A: (a) the three-digit area code has its middle digit 0 or 1.     Then, for the first digit, 0 or 1 is…

Q: Sketch the curve with polar equation r = cos(30), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and…

A:

Q: Exercise 5.5.2 Let T be a linear transformation given by -1 2 21 Is T one to one? Is T onto? T X = X

A:

Q: Use Green’s Theorem to prove the area of an ellipse with semi-major and semi-minor axes lengths a…

A:

Q: The set is given below. 0 = {x E R², || x ||² < 25} Where || x ||² is square of the Euclidian norm…

A:

Q: uniformly continuous: 1) f(x) = (x*ln(x))/(1+x^(2)) on [0,infinity) 2) f(x) = (x)/(1+sqrt(x)) on…

A:

Q: We know that A = 7 2 77 b= -53 88 M = 4 2 8 -1 -30 2 9 Find M31- Write system of equation Ax = b in…

A:

Q: 70. Displacement from a velocity graph Consider the velocity function for an object moving along a…

A:

Q: 4. List all solutions in polar form of the equation x5 = 3 in the complex numbers. (Start by finding…

A:

Q: Let C[0, 1] be the collection of continuous functions on the closed interval [0, 1]. Decide which of…

A: Let C[0, 1] be the collection of continuous functions on the closed interval [0, 1]. Decide which of…

Q: 2. The initial value problem √4-zy" +=e, y(1) = -1, g(1) = 0 is certain to have a unique solution on…

A: Existence and Uniqueness Theorem Consider the IVP     y''+p(x)y'+q(x)y= r(x) with…

Q: Consider z = f(x,y) = x2 + 3xy + e2y. Find the equation of the tangent when x = 1 and y = 0.   Find…

A:

Q: Find an SVD of the indicated matrix. (Enter each matrix in the form [[row 1], [row 2], ...], where…

A:

Q: Describe all least-squares solutions of the equation Ax = b. 1 10 1 10 1 A = b= 101 101 1 3 6 8 The…

A:

Q: Over the time interval 0 ≤ t ≤ 15, (t is in hours) water is being pumped into a tank at a constant…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Suppose f(x) > 0 and continuous for all x except x = 3, and Select the integrals that will…

A:

Q: Use the - definition to show the following limits: (c) lim x-0 x+p=√p X = 2√ √/p' P> 0.

A:

Q: Theorem 1.5. The principal normals at consecutive points of a curve do not intersect unless t = 0)

A:

Q: Using Delta Epsilon Proof sin x 2. Prove: lim x-0 1.

A:

Q: Use the table to determine if the pattern of change is linear or exponential. If the change is…

A:

Q: 4. The series n=0 1-5m² n *** (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

A: Solution:-

Q: Exercise 5.7.5 Let T be a linear transformation given by What is dim(ker (T))? +B-008 1 X y Z X Z.

A:

Q: Reduce each of the following to the smallest non-negative residual. (a) 87122 mod 23 (b) -7823 mod…

A:

Q: 22. A couple inherits $89,000. How much can this generate at the beginning of each month over the…

A:

Q: same pentagonal base as the pyramid, what is the volume of the prism? Round your answer to one…

A:

Q: which quarant in the complex plane would the result of the product, z1.z2 of the complex numbers…

A: Given the complex numbers              z1=3cis 85, and  z2=6cis205.

Q: 2) Compute the determinant of the following matrix: A = 00003 00034 00121 01221 22314

A:

Q: (b) Compute the flux of the vector field F(x, y, z) = yi + zk upwards through portion of the cone z…

A:

Q: 3. Use Green's Theorem to evaluate the line integral ſxy¹dx+ 2xydy, where C is the portion of the…

A: Let     M(x,y) = xy4      and    Nx,y = 2xy                     ∂M∂y=4xy3     and      ∂N∂x =…

Q: 2. Calculate [(yz+1)dx+xz dy + xydz, where C consists of line segments from (0,0,0) to (1,0,1) and…

A:

Q: Find the minimum distance from the plane x + y + z = 1 to the point (2, 1, 1).

A:

Q: Theorem 1.5. The principal normals at consecutive points of a curve do not intersect unless t = 0

A:

Q: The numbers of domestic and international flights for three airlines for the year 2012 are given in…

A: From given data we have              The chances for airline A That domestic m = 517893…

Q: Use Theorem 7.4.2 to evaluate the given Laplace transform. Do not evaluate the convolution integral…

A:

Q: Let g(x) be the function graphed below. -10--8-7 dy da k = 10 9 8 1 564 7 m TH ₁ 80 1 4-8 79 6- 10…

A:

Q: 12. F(x, y, z) = yi+zj + xk, S is the helicoid with vector equation r(u, v) = u cos vi+usin vj +…

A:

Q: Suppose a triangle has the following vertices: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0) What…

A:

Q: a. 1+3+5+7+ b. 4+9+14+ c. 3+8+13+. d. + 1 1.2 1 2.3 ... + ·· +44 +63 1 3.4 +99 + + 1 49.50

A:

Q: Find the exact value that the sequence Σ(n=0, ∞) sinn 1 converges to. (Note n=0 that as usual, sinn…

A: As per the question we are given an infinite series as : Σ(n=0, ∞) sinn 1 whose exact value we have…

Q: A = 060 4 1 2 20 04

A:

Q: Problem 2. Sketch the set of points x = (₁, ₂) in R² such that (i) ||x||2 = 1, (ii) ||x||₁ = 1,…

A:

Q: 1. Consider the function y = 7 cos[(x −)] +3 a. What is the amplitude? b. What is the period? c.…

A:

Q: Separation of Variables Sote the separable equation: cosx cosy du se 2=-=-=-* du sin(x) y

A:

Q: Compute ae in (Z/n)* using only multiplication and division for the following a, e, n: (a) a = 10…

A: For (a), We are given that a=10, e=5, and n=9350647. Here, we will be computing ae! in (ℤ/n)× using…